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Welcome to the Friday edition of our newsletter. We spend Fridays going deeper into tools and trends related to generative AI (and Tuesdays sharing news updates). This week, Professor Porter looks at OpenAI’s recent avalanche of mathematical breakthroughs, the concerns they’ve raised among mathematicians, and what they can teach us about the hidden costs of automation.

Although I (Porter) primarily spend my working hours directing Drake’s AI program and helping folks in the community build a foundation of AI literacy that develops into AI proficiency, I’m a mathematician by training. And I still love to geek out about the newest developments in mathematics, particularly in my own areas of specialty (computability theory and, more specifically, algorithmic randomness, for those of you tracking these sorts of things).

With that combo of interests, you’d think I’d be thrilled with the latest news about the forefront of AI and research mathematics, as OpenAI posted just last week a whopping 719 research manuscripts purporting to solve 372 families of open mathematics problems from essentially every branch of pure mathematics (including my own). But…I wasn’t. To be honest, I was a bit shellshocked. And I’d like to explain why. Read on below to learn more about what transpired last week, how the mathematical community has responded to it, and what we can potentially learn about the cost of automation.

Here’s a bit more background on what led to OpenAI’s announcement of the massive bundle of theorems it released last week.

First, on September 8, OpenAI announced the solution of the Navier-Stokes problem, one of seven Millennium Prize problems isolated by the Clay Mathematics Institute in May 2000 as significant open problems “that have resisted solution over the years.” Setting aside an ongoing controversy about whether OpenAI accessed work of a team of mathematicians that had used their platform to make progress on the problem, the response from the mathematics community was not one of celebration, but rather one of deep concern. Just three days after the Navier-Stokes solution was announced, a group of 28 Fields Medalists (the equivalent of Nobel Prize winners in the mathematics community) published an open letter, “A Severe Misalignment of AI in Mathematics.”

In the opening paragraph of the letter, these mathematicians threw down their gauntlet, stating that “the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community.” Their concern, which I’ll explain shortly, is that these AI-driven developments threaten to reduce the practice of mathematics to simply solving problems, rather than developing “understanding and the ability to formulate new questions and ideas,” as the Fields Medalists put it.

Fast-forward to last week, on October 6 to be exact, when OpenAI’s announcement “Sharing AI progress in mathematics” heralded the release of the tranche of AI-generated manuscripts containing purported proofs of many important questions from areas such as algebra, theoretical computer science, mathematical physics, probability theory, number theory, and multiple branches of geometry that you might not have known existed.

The New York Times covered the release in “‘Breathtaking,’ ‘Devastating’: Mathematics Reels After New OpenAI Release,” in which we find Oxford mathematician Martin Bridson describing these results as “exciting for many, frightening for others, and devastating for some.”

Let me try to illustrate the situation with an analogy inspired by an X post that I found helpful.

Imagine you are a paleontologist who has just discovered a site that contains T. rex remains. Suppose further that a rogue maverick who yearns for paleontological glory learns of your site and decides to farm out the excavation work to a new company that can efficiently extract any bones, carefully clean them, and rapidly ship them to any museum of one’s choice to be reconstructed and displayed. The maverick commissions the work, and the excavation is completed before you can even get started. While the maverick revels in the display of the T. rex, you lament not just the loss of the discovery, but the loss of so much other information: the configuration of the bones in the ground, trace fossils like footprints and burrows, the composition of the rock strata, and the chemical properties of the surrounding rocks. Yes, the bones have been recovered, but so much of the story has been lost: how the T. rex arrived at the site, what might have led to its death, what its environment looked like, and all the subsequent research that could have followed from this information. All of this was sacrificed in the reduction of paleontology to the mere extraction of bones.

This captures an important concern among mathematicians about the OpenAI developments. The practice of doing mathematics cannot be simply reduced to proving theorems. There is so much value in the intermediate steps of mathematical research that one takes to arrive at a solution, which often open new lines of inquiry, new questions to explore, new connections to previous work, and potentially even new theories inspired by this work. As described by mathematician Terry Tao, one of the Fields Medalists referenced above, it’s like watching only the beginning and ending of a movie: “Technically, all the plot lines are resolved, but most of the value of the experience was lost.” This is such as serious concern that some mathematicians have even formed the Association for Human Mathematicians to protect “mathematics as a human endeavor against the threat of artificial intelligence.”

There are other causes for concern. For instance, who is going to verify these theorems? The process of refereeing mathematical results is slow and arduous, and OpenAI’s proofs are reportedly not the most clearly written. Suddenly, potentially thousands of hours of uncompensated refereeing work has been foisted upon the mathematical community. And which journals will even publish these results? Moreover, with no human author to vouch for these results, who will present these findings at various mathematics conferences (one of the primary ways to disseminate new mathematical developments)?

The vast majority of our readers are not working mathematicians. But nearly all of you work in some capacity, and AI is increasingly becoming part of that work. Here are some lessons from OpenAI’s mathematical avalanche that we might put into practice.

Value the process as much as the product: AI is particularly helpful with routine, rote, boilerplate tasks, where the process of completing that task is purely instrumental. But when the process itself has value beyond the final product, particularly when our own participation is fundamental to that value, we need to be careful about what we automate.

Make more room for what makes us human: For many of us, much of our work involves distinctly human qualities that cannot be replicated through automation, such as social relationships, organizational savvy, aesthetic sensibility, or simply our own unique idiosyncrasies. Lean into these human aspects of your work, particularly when AI can free up more of your time to cultivate them rather than replace them.

Efficiency isn't the same as progress: The mathematics community has been forced to grapple with what counts as progress in the field, and it’s clear that the answer isn’t simply the number of theorems published. Producing more, working faster, and checking off more boxes are all easy to measure, but they don't necessarily tell us whether we're accomplishing anything more meaningful. In our own work, what might we be tempted to mistake for progress simply because it makes us more efficient?

Don't automate away opportunities to learn: As much as we hate to admit it, we often learn by trial and error. The missteps, wrong turns, and unexpected obstacles we encounter along the way can teach us as much as reaching the finish line. When we hand these tasks over to AI, we risk depriving ourselves of the very experiences that help us develop expertise, sharpen our judgment, and discover new ways to solve problems.

Someone still needs to understand the output: Generating a result is only part of the work. Whether we're proving mathematical theorems, analyzing financial data, or developing business strategies, someone needs to be able to evaluate, explain, and take responsibility for what AI produces. An answer that nobody has taken time to internalize or verify might create more work than it saves.

The saga of OpenAI’s mathematical avalanche is likely just getting started, with more bundles of results rumored to come, and even an announcement yesterday that OpenAI will donate $5 million to support workshops and conferences for mathematicians to understand and build upon results generated by AI (in partnership with the Simons Foundation and rival AI company Anthropic). Whether this avalanche ultimately advances mathematics or buries something essential about the practice of mathematics may depend less on what AI can accomplish than on what we choose to do with it.